Subgroups — C₃×C₅×D₃×C₂²⋊C₄ #13087892

Order 1440.

562 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×D₃	C₂	1	2	yes	maximal, complemented
3	C₃²×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#217	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×C₅×C₂²⋊C₄	—	3	1	no	maximal
7	C₅×D₃×C₂²⋊C₄	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂³×C₃²×C₅	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₅×D₃	—	2	4	no	—
10	C₂²×C₃×C₅×D₃	C₄	1	4	yes	complemented
11	C₂²×C₃×C₅×D₃	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×D₃	C₂²	1	1	yes	characteristic
13	C₂×C₃²×C₄×C₅	C₂²	1	2	yes	complemented
14	C₂×C₃×C₅×Dic₃	C₂²	1	2	yes	complemented
15	C₃×C₄×C₅×D₃	—	2	4	no	—
16	C₃×D₃×C₂²⋊C₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂⁴×C₃×C₅	—	3	1	no	—
18	C₂³×C₅×D₃	C₂×C₃	1	1	yes	characteristic
19	C₂²×C₃×C₄×C₅	—	3	2	no	—
20	C₂×C₄×C₅×D₃	C₂×C₃	1	2	yes	complemented
21	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
22	C₃×C₅×C₂²⋊C₄	—	3	1	no	—
23	C₃×C₅×C₂²⋊C₄	—	3	2	no	—
24	C₃×C₅×C₂²⋊C₄	D₃	1	1	yes	characteristic, direct product factor
25	C₃×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
26	C₅×#217	C₂×C₃	1	1	yes	characteristic, complemented
27	C₅×(C₂×D₃)⋊C₄	C₂×C₃	1	2	yes	complemented
28	C₂²×C₃²×C₅	—	2	2	no	—
29	C₂²×C₃²×C₅	C₂×C₄	1	2	yes	complemented
30	C₂²×C₃²×C₅	C₂³	1	1	yes	characteristic
31	C₂×C₃×C₅×D₃	—	2	2	no	—
32	C₂×C₃×C₅×D₃	—	2	8	no	—
33	C₂×C₃×C₅×D₃	C₂×C₄	1	2	yes	—
34	C₂×C₃×C₅×D₃	C₂×C₄	1	2	yes	complemented
35	C₂×C₃×C₅×D₃	D₄	1	4	yes	—
36	C₃²×C₄×C₅	—	2	2	no	—
37	C₃×C₅×Dic₃	—	2	2	no	—
38	C₂×C₅×C₂²⋊C₄	—	3	1	no	Hall
39	C₂³×C₃×D₃	C₂×C₅	1	1	yes	characteristic
40	C₂×C₃×C₄×D₃	C₂×C₅	1	2	yes	complemented
41	C₃²×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
42	C₃×#217	C₂×C₅	1	1	yes	characteristic, complemented
43	C₃×(C₂×D₃)⋊C₄	C₂×C₅	1	2	yes	complemented
44	C₂³×C₃×C₅	—	2	1	no	—
45	C₂³×C₃×C₅	—	3	1	no	—
46	C₂³×C₃×C₅	—	3	4	no	—
47	C₂³×C₃×C₅	—	3	1	no	—
48	C₂³×C₃×C₅	—	6	4	no	—
49	C₂³×C₃×C₅	C₂×D₃	1	1	yes	characteristic
50	C₂³×C₃×C₅	C₂²×C₃	1	1	yes	characteristic
51	C₂²×C₅×D₃	—	2	4	no	—
52	C₂²×C₅×D₃	C₃×C₄	1	4	yes	complemented
53	C₂²×C₅×D₃	C₂²×C₃	1	1	yes	characteristic
54	C₂²×C₅×D₃	C₂²×C₃	1	1	yes	characteristic
55	C₂×C₃×C₄×C₅	—	2	2	no	—
56	C₂×C₃×C₄×C₅	—	3	2	no	—
57	C₂×C₃×C₄×C₅	—	6	4	no	—
58	C₂×C₃×C₄×C₅	C₂×D₃	1	2	yes	complemented
59	C₂×C₃×C₄×C₅	C₂²×C₃	1	2	yes	complemented
60	C₂×C₅×Dic₃	C₂²×C₃	1	2	yes	complemented
61	C₄×C₅×D₃	—	2	4	no	—
62	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
63	D₃×C₂²⋊C₄	C₃×C₅	1	1	yes	characteristic, direct product factor
64	C₂×C₃²×C₅	—	2	2	no	—
65	C₂×C₃²×C₅	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₃²×C₅	C₂×D₄	1	2	yes	—
67	C₃×C₅×D₃	—	2	2	no	—
68	C₃×C₅×D₃	C₂²⋊C₄	1	4	yes	direct product factor
69	C₂⁴×C₅	—	3	1	no	—
70	C₂²×C₄×C₅	—	3	2	no	—
71	C₅×C₂²⋊C₄	—	3	1	no	—
72	C₅×C₂²⋊C₄	—	3	2	no	—
73	C₅×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic, direct product factor
74	C₂³×C₃²	C₂²×C₅	1	1	yes	characteristic
75	C₂²×C₃×D₃	—	2	4	no	—
76	C₂²×C₃×D₃	C₄×C₅	1	4	yes	complemented
77	C₂²×C₃×D₃	C₂²×C₅	1	1	yes	characteristic
78	C₂²×C₃×D₃	C₂²×C₅	1	1	yes	characteristic
79	C₂×C₃²×C₄	C₂²×C₅	1	2	yes	complemented
80	C₂×C₃×Dic₃	C₂²×C₅	1	2	yes	complemented
81	C₃×C₄×D₃	—	2	4	no	—
82	C₂²×C₃×C₅	—	2	2	no	—
83	C₂²×C₃×C₅	—	2	2	no	—
84	C₂²×C₃×C₅	—	2	2	no	—
85	C₂²×C₃×C₅	—	2	1	no	—
86	C₂²×C₃×C₅	—	3	2	no	—
87	C₂²×C₃×C₅	—	3	4	no	—
88	C₂²×C₃×C₅	—	3	2	no	—
89	C₂²×C₃×C₅	—	4	2	no	—
90	C₂²×C₃×C₅	—	6	8	no	—
91	C₂²×C₃×C₅	—	6	2	no	—
92	C₂²×C₃×C₅	C₄×D₃	1	2	yes	complemented
93	C₂²×C₃×C₅	C₂×C₃×C₄	1	2	yes	complemented
94	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
95	C₂²×C₃×C₅	C₂³×C₃	1	1	yes	characteristic
96	C₂×C₅×D₃	—	2	2	no	—
97	C₂×C₅×D₃	—	2	8	no	—
98	C₂×C₅×D₃	C₂×C₃×C₄	1	2	yes	—
99	C₂×C₅×D₃	C₂×C₃×C₄	1	2	yes	complemented
100	C₂×C₅×D₃	C₃×D₄	1	4	yes	—
101	C₃×C₄×C₅	—	2	2	no	—
102	C₃×C₄×C₅	—	2	2	no	—
103	C₃×C₄×C₅	—	4	2	no	—
104	C₃×C₄×C₅	—	6	2	no	—
105	C₅×Dic₃	—	2	2	no	—
106	C₂⁴×C₃	—	3	1	no	—
107	C₂³×D₃	C₂×C₃×C₅	1	1	yes	characteristic
108	C₂²×C₃×C₄	—	3	2	no	—
109	C₂×C₄×D₃	C₂×C₃×C₅	1	2	yes	complemented
110	C₃×C₂²⋊C₄	—	2	1	no	—
111	C₃×C₂²⋊C₄	—	3	1	no	—
112	C₃×C₂²⋊C₄	—	3	2	no	—
113	C₃×C₂²⋊C₄	C₅×D₃	1	1	yes	characteristic, direct product factor
114	C₃×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
115	#217	C₂×C₃×C₅	1	1	yes	characteristic, complemented
116	(C₂×D₃)⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
117	C₃²×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
118	C₂³×C₅	—	3	1	no	—
119	C₂³×C₅	—	3	4	no	—
120	C₂³×C₅	—	3	1	no	—
121	C₂³×C₅	—	6	4	no	—
122	C₂³×C₅	C₂×C₃×D₃	1	1	yes	characteristic
123	C₂×C₄×C₅	—	3	2	no	—
124	C₂×C₄×C₅	—	6	4	no	—
125	C₂×C₄×C₅	C₂×C₃×D₃	1	2	yes	complemented
126	C₂²×C₃²	—	2	2	no	—
127	C₂²×C₃²	C₂×C₄×C₅	1	2	yes	complemented
128	C₂²×C₃²	C₂³×C₅	1	1	yes	characteristic
129	C₂×C₃×D₃	—	2	2	no	—
130	C₂×C₃×D₃	—	2	8	no	—
131	C₂×C₃×D₃	C₂×C₄×C₅	1	2	yes	—
132	C₂×C₃×D₃	C₂×C₄×C₅	1	2	yes	complemented
133	C₂×C₃×D₃	C₅×D₄	1	4	yes	—
134	C₃²×C₄	—	2	2	no	—
135	C₃×Dic₃	—	2	2	no	—
136	C₂×C₂²⋊C₄	—	3	1	no	Sylow
137	C₂×C₃×C₅	—	2	2	no	—
138	C₂×C₃×C₅	—	2	2	no	—
139	C₂×C₃×C₅	—	2	1	no	—
140	C₂×C₃×C₅	—	2	2	no	—
141	C₂×C₃×C₅	—	3	4	no	—
142	C₂×C₃×C₅	—	4	2	no	—
143	C₂×C₃×C₅	—	6	2	no	—
144	C₂×C₃×C₅	C₂×C₄×D₃	1	1	yes	characteristic
145	C₂×C₃×C₅	D₃×D₄	1	2	yes	—
146	C₂×C₃×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
147	C₂×C₃×C₅	C₂×C₃×D₄	1	2	yes	—
148	C₅×D₃	—	2	2	no	—
149	C₅×D₃	C₃×C₂²⋊C₄	1	4	yes	direct product factor
150	C₂³×C₃	—	2	1	no	—
151	C₂³×C₃	—	3	1	no	—
152	C₂³×C₃	—	3	4	no	—
153	C₂³×C₃	—	3	1	no	—
154	C₂³×C₃	—	6	4	no	—
155	C₂³×C₃	C₂×C₅×D₃	1	1	yes	characteristic
156	C₂³×C₃	C₂²×C₃×C₅	1	1	yes	characteristic
157	C₂²×D₃	—	2	4	no	—
158	C₂²×D₃	C₃×C₄×C₅	1	4	yes	complemented
159	C₂²×D₃	C₂²×C₃×C₅	1	1	yes	characteristic
160	C₂²×D₃	C₂²×C₃×C₅	1	1	yes	characteristic
161	C₂×C₃×C₄	—	2	2	no	—
162	C₂×C₃×C₄	—	3	2	no	—
163	C₂×C₃×C₄	—	6	4	no	—
164	C₂×C₃×C₄	C₂×C₅×D₃	1	2	yes	complemented
165	C₂×C₃×C₄	C₂²×C₃×C₅	1	2	yes	complemented
166	C₂×Dic₃	C₂²×C₃×C₅	1	2	yes	complemented
167	C₄×D₃	—	2	4	no	—
168	C₂²×C₅	—	2	2	no	—
169	C₂²×C₅	—	3	2	no	—
170	C₂²×C₅	—	3	4	no	—
171	C₂²×C₅	—	3	2	no	—
172	C₂²×C₅	—	6	8	no	—
173	C₂²×C₅	—	6	2	no	—
174	C₂²×C₅	C₃×C₄×D₃	1	2	yes	complemented
175	C₂²×C₅	C₂²×C₃×D₃	1	1	yes	characteristic
176	C₄×C₅	—	2	2	no	—
177	C₄×C₅	—	6	2	no	—
178	C₂×C₃²	—	2	2	no	—
179	C₂×C₃²	C₂²×C₄×C₅	1	1	yes	characteristic
180	C₂×C₃²	C₂×C₅×D₄	1	2	yes	—
181	C₃×D₃	—	2	2	no	—
182	C₃×D₃	C₅×C₂²⋊C₄	1	4	yes	direct product factor
183	C₂⁴	—	3	1	no	—
184	C₂²×C₄	—	3	2	no	—
185	C₂²⋊C₄	—	3	1	no	—
186	C₂²⋊C₄	—	3	2	no	—
187	C₂²⋊C₄	C₃×C₅×D₃	1	1	yes	characteristic, direct product factor
188	C₃×C₅	—	2	1	no	—
189	C₃×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic, direct product factor
190	C₃×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic, complemented
191	C₂²×C₃	—	2	2	no	—
192	C₂²×C₃	—	2	2	no	—
193	C₂²×C₃	—	2	2	no	—
194	C₂²×C₃	—	2	1	no	—
195	C₂²×C₃	—	3	2	no	—
196	C₂²×C₃	—	3	4	no	—
197	C₂²×C₃	—	3	2	no	—
198	C₂²×C₃	—	4	2	no	—
199	C₂²×C₃	—	6	8	no	—
200	C₂²×C₃	—	6	2	no	—
201	C₂²×C₃	C₄×C₅×D₃	1	2	yes	complemented
202	C₂²×C₃	C₂×C₃×C₄×C₅	1	2	yes	complemented
203	C₂²×C₃	C₂²×C₅×D₃	1	1	yes	characteristic
204	C₂²×C₃	C₂³×C₃×C₅	1	1	yes	characteristic
205	C₂×D₃	—	2	2	no	—
206	C₂×D₃	—	2	8	no	—
207	C₂×D₃	C₂×C₃×C₄×C₅	1	2	yes	—
208	C₂×D₃	C₂×C₃×C₄×C₅	1	2	yes	complemented
209	C₂×D₃	C₃×C₅×D₄	1	4	yes	—
210	C₃×C₄	—	2	2	no	—
211	C₃×C₄	—	2	2	no	—
212	C₃×C₄	—	4	2	no	—
213	C₃×C₄	—	6	2	no	—
214	Dic₃	—	2	2	no	—
215	C₂×C₅	—	2	2	no	—
216	C₂×C₅	—	3	4	no	—
217	C₂×C₅	—	6	2	no	—
218	C₂×C₅	C₂×C₃×C₄×D₃	1	1	yes	characteristic
219	C₂×C₅	C₃×D₃×D₄	1	2	yes	—
220	C₃²	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
221	C₂³	—	3	1	no	—
222	C₂³	—	3	4	no	—
223	C₂³	—	3	1	no	—
224	C₂³	—	6	4	no	—
225	C₂³	C₂×C₃×C₅×D₃	1	1	yes	characteristic
226	C₂×C₄	—	3	2	no	—
227	C₂×C₄	—	6	4	no	—
228	C₂×C₄	C₂×C₃×C₅×D₃	1	2	yes	complemented
229	C₂×C₃	—	2	2	no	—
230	C₂×C₃	—	2	2	no	—
231	C₂×C₃	—	2	1	no	—
232	C₂×C₃	—	2	2	no	—
233	C₂×C₃	—	3	4	no	—
234	C₂×C₃	—	4	2	no	—
235	C₂×C₃	—	6	2	no	—
236	C₂×C₃	C₂×C₄×C₅×D₃	1	1	yes	characteristic
237	C₂×C₃	C₅×D₃×D₄	1	2	yes	—
238	C₂×C₃	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
239	C₂×C₃	C₂×C₃×C₅×D₄	1	2	yes	—
240	D₃	—	2	2	no	—
241	D₃	C₃×C₅×C₂²⋊C₄	1	4	yes	direct product factor
242	C₅	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
243	C₂²	—	2	2	no	—
244	C₂²	—	3	2	no	—
245	C₂²	—	3	4	no	—
246	C₂²	—	3	2	no	—
247	C₂²	—	6	8	no	—
248	C₂²	—	6	2	no	—
249	C₂²	C₃×C₄×C₅×D₃	1	2	yes	complemented
250	C₂²	C₂²×C₃×C₅×D₃	1	1	yes	characteristic
251	C₄	—	2	2	no	—
252	C₄	—	6	2	no	—
253	C₃	—	2	1	no	—
254	C₃	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic, direct product factor
255	C₃	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic, complemented
256	C₂	—	2	2	no	—
257	C₂	—	3	4	no	—
258	C₂	—	6	2	no	—
259	C₂	C₂×C₃×C₄×C₅×D₃	1	1	yes	characteristic
260	C₂	C₃×C₅×D₃×D₄	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₅	C₂²×D₃
commutator	C₂×C₃	C₂²×C₃×C₄×C₅
Frattini	C₂²	C₂²×C₃×C₅×D₃
Fitting	C₃²×C₅×C₂²⋊C₄	C₂
socle	C₂²×C₃²×C₅	C₂³
prime radical	C₂³×C₃×C₅×D₃	C₂
cosocle	C₂²×C₃	C₂³×C₃×C₅
hypercenter	C₃×C₅×C₂²⋊C₄	D₃
hypocenter	C₃	C₂×C₃×C₅×C₂²⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×C₂²⋊C₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₃×C₄×C₅×D₃	C₂	semidirect
3. C₃²×C₅×C₂²⋊C₄	C₂	semidirect
4. C₃×C₅×#217	C₂	semidirect
5. C₃×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
7. C₅×D₃×C₂²⋊C₄	C₃	direct (N × H)
10. C₂²×C₃×C₅×D₃	C₄	semidirect
13. C₂×C₃²×C₄×C₅	C₂²	semidirect
14. C₂×C₃×C₅×Dic₃	C₂²	semidirect
16. C₃×D₃×C₂²⋊C₄	C₅	direct (N × H)
20. C₂×C₄×C₅×D₃	C₂×C₃	semidirect
24. C₃×C₅×C₂²⋊C₄	D₃	direct (N × H)
25. C₃×C₅×C₂²⋊C₄	C₂×C₃	semidirect
26. C₅×#217	C₂×C₃	semidirect
27. C₅×(C₂×D₃)⋊C₄	C₂×C₃	semidirect
29. C₂²×C₃²×C₅	C₂×C₄	semidirect
34. C₂×C₃×C₅×D₃	C₂×C₄	semidirect
40. C₂×C₃×C₄×D₃	C₂×C₅	semidirect
41. C₃²×C₂²⋊C₄	C₂×C₅	semidirect
42. C₃×#217	C₂×C₅	semidirect
43. C₃×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
52. C₂²×C₅×D₃	C₃×C₄	semidirect
58. C₂×C₃×C₄×C₅	C₂×D₃	semidirect
59. C₂×C₃×C₄×C₅	C₂²×C₃	semidirect
60. C₂×C₅×Dic₃	C₂²×C₃	semidirect
63. D₃×C₂²⋊C₄	C₃×C₅	direct (N × H)
68. C₃×C₅×D₃	C₂²⋊C₄	direct (N × H)
73. C₅×C₂²⋊C₄	C₃×D₃	direct (N × H)
76. C₂²×C₃×D₃	C₄×C₅	semidirect
79. C₂×C₃²×C₄	C₂²×C₅	semidirect
80. C₂×C₃×Dic₃	C₂²×C₅	semidirect
92. C₂²×C₃×C₅	C₄×D₃	semidirect
93. C₂²×C₃×C₅	C₂×C₃×C₄	semidirect
99. C₂×C₅×D₃	C₂×C₃×C₄	semidirect
109. C₂×C₄×D₃	C₂×C₃×C₅	semidirect
113. C₃×C₂²⋊C₄	C₅×D₃	direct (N × H)
114. C₃×C₂²⋊C₄	C₂×C₃×C₅	semidirect
115. #217	C₂×C₃×C₅	semidirect
116. (C₂×D₃)⋊C₄	C₂×C₃×C₅	semidirect
117. C₃²×C₅	C₂×C₂²⋊C₄	semidirect
125. C₂×C₄×C₅	C₂×C₃×D₃	semidirect
127. C₂²×C₃²	C₂×C₄×C₅	semidirect
132. C₂×C₃×D₃	C₂×C₄×C₅	semidirect
149. C₅×D₃	C₃×C₂²⋊C₄	direct (N × H)
158. C₂²×D₃	C₃×C₄×C₅	semidirect
164. C₂×C₃×C₄	C₂×C₅×D₃	semidirect
165. C₂×C₃×C₄	C₂²×C₃×C₅	semidirect
166. C₂×Dic₃	C₂²×C₃×C₅	semidirect
174. C₂²×C₅	C₃×C₄×D₃	semidirect
182. C₃×D₃	C₅×C₂²⋊C₄	direct (N × H)
187. C₂²⋊C₄	C₃×C₅×D₃	direct (N × H)
189. C₃×C₅	D₃×C₂²⋊C₄	direct (N × H)
190. C₃×C₅	C₂×C₃×C₂²⋊C₄	semidirect
201. C₂²×C₃	C₄×C₅×D₃	semidirect
202. C₂²×C₃	C₂×C₃×C₄×C₅	semidirect
208. C₂×D₃	C₂×C₃×C₄×C₅	semidirect
220. C₃²	C₂×C₅×C₂²⋊C₄	semidirect
228. C₂×C₄	C₂×C₃×C₅×D₃	semidirect
241. D₃	C₃×C₅×C₂²⋊C₄	direct (N × H)
242. C₅	C₃×D₃×C₂²⋊C₄	direct (N × H)
249. C₂²	C₃×C₄×C₅×D₃	semidirect
254. C₃	C₅×D₃×C₂²⋊C₄	direct (N × H)
255. C₃	C₂×C₃×C₅×C₂²⋊C₄	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₃×C₅×D₃	2
C₂×C₃×C₄×C₅×D₃	2
C₃²×C₅×C₂²⋊C₄	2
C₃×C₅×#217	2
C₃×C₅×(C₂×D₃)⋊C₄	2
C₂×C₃×C₅×C₂²⋊C₄	3
C₅×D₃×C₂²⋊C₄	3
C₃×D₃×C₂²⋊C₄	5

Subgroups — C3×C5×D3×C22⋊C4 #13087892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₃×C₂²⋊C₄ #13087892